9349 = (2 * 4674) + 1 ;
hence not 2 divides 9349 by NAT_4:9; :: thesis:
9349 = (3 * 3116) + 1 ;
hence not 3 divides 9349 by NAT_4:9; :: thesis:
9349 = (5 * 1869) + 4 ;
hence not 5 divides 9349 by NAT_4:9; :: thesis:
9349 = (7 * 1335) + 4 ;
hence not 7 divides 9349 by NAT_4:9; :: thesis:
9349 = (11 * 849) + 10 ;
hence not 11 divides 9349 by NAT_4:9; :: thesis:
9349 = (13 * 719) + 2 ;
hence not 13 divides 9349 by NAT_4:9; :: thesis:
9349 = (17 * 549) + 16 ;
hence not 17 divides 9349 by NAT_4:9; :: thesis:
9349 = (19 * 492) + 1 ;
hence not 19 divides 9349 by NAT_4:9; :: thesis:
9349 = (23 * 406) + 11 ;
hence not 23 divides 9349 by NAT_4:9; :: thesis:
9349 = (29 * 322) + 11 ;
hence not 29 divides 9349 by NAT_4:9; :: thesis:
9349 = (31 * 301) + 18 ;
hence not 31 divides 9349 by NAT_4:9; :: thesis:
9349 = (37 * 252) + 25 ;
hence not 37 divides 9349 by NAT_4:9; :: thesis:
9349 = (41 * 228) + 1 ;
hence not 41 divides 9349 by NAT_4:9; :: thesis:
9349 = (43 * 217) + 18 ;
hence not 43 divides 9349 by NAT_4:9; :: thesis:
9349 = (47 * 198) + 43 ;
hence not 47 divides 9349 by NAT_4:9; :: thesis:
9349 = (53 * 176) + 21 ;
hence not 53 divides 9349 by NAT_4:9; :: thesis:
9349 = (59 * 158) + 27 ;
hence not 59 divides 9349 by NAT_4:9; :: thesis:
9349 = (61 * 153) + 16 ;
hence not 61 divides 9349 by NAT_4:9; :: thesis:
9349 = (67 * 139) + 36 ;
hence not 67 divides 9349 by NAT_4:9; :: thesis:
9349 = (71 * 131) + 48 ;
hence not 71 divides 9349 by NAT_4:9; :: thesis:
9349 = (73 * 128) + 5 ;
hence not 73 divides 9349 by NAT_4:9; :: thesis:
9349 = (79 * 118) + 27 ;
hence not 79 divides 9349 by NAT_4:9; :: thesis:
9349 = (83 * 112) + 53 ;
hence not 83 divides 9349 by NAT_4:9; :: thesis:
9349 = (89 * 105) + 4 ;
hence not 89 divides 9349 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9349 & n is prime holds
not n divides 9349 by XPRIMET1:48;
hence 9349 is prime by NAT_4:14; :: thesis: